I wonder if it would be feasable to simulate on the clients and server and send occasional absolute positions and correct the cars over time.

Yes, this can work. If the cars are "scenery" and seldom actually collide, and/or don't matter much for the gameplay, then users might not care about the occasional inconsistencies. If the cars are an essential part of gameplay, users may feel that it's "too glitchy," though.

This is how we've handled games in the past, but always the exact position has been non-critical.

Each person transmits their location as game data rather than as Unity-managed object positions. The other players are treated as any other NPC. When an event comes in that a remote player has moved, their avatar is given a command that is basically avatar.MoveTo(location, direction). It may cause weird situations where the remote player's avatar needs to do pathfinding and run around the map, and very rarely it hits a critically-bad situation and the simulator will simply force the avatar to the location without concern for correctness and mapping.

Works well in games where players are not seeing the same screen and don't care too much about collisions. I imagine that same method would fail horribly for any kind of driving and crashing situation.